spectral_analysis_rad_max

Complexity

Total Complexity

0

Size/Duplication

Total Lines	347
Duplicated Lines	0 %

Importance

Changes

0

"""
Spectral analysis with energy-dependent directional cuts
========================================================

Perform a point like spectral analysis with energy dependent offset cut.


Prerequisites
-------------

-  Understanding the basic data reduction performed in the
   :doc:`/tutorials/analysis-1d/spectral_analysis` tutorial.
-  understanding the difference between a
   `point-like <https://gamma-astro-data-formats.readthedocs.io/en/latest/irfs/point_like/index.html>`__
   and a
   `full-enclosure <https://gamma-astro-data-formats.readthedocs.io/en/latest/irfs/full_enclosure/index.html>`__
   IRF.

Context
-------

As already explained in the :doc:`/tutorials/analysis-1d/spectral_analysis`
tutorial, the background is estimated fromthe field of view of the observation.
In particular, the source and background events are counted within a circular 
ON region enclosing the source. The background to be subtracted is then estimated
from one or more OFF regions with an expected background rate similar to the one
in the ON region (i.e. from regions with similar acceptance).

*Full-containment* IRFs have no directional cut applied, when employed
for a 1D analysis, it is required to apply a correction to the IRF
accounting for flux leaking out of the ON region. This correction is
typically obtained by integrating the PSF within the ON region.

When computing a *point-like* IRFs, a directional cut around the assumed
source position is applied to the simulated events. For this IRF type,
no PSF component is provided. The size of the ON and OFF regions used
for the spectrum extraction should then reflect this cut, since a
response computed within a specific region around the source is being
provided.

The directional cut is typically an angular distance from the assumed
source position, :math:`\\theta`. The
`gamma-astro-data-format <https://gamma-astro-data-formats.readthedocs.io/en/latest/>`__
specifications offer two different ways to store this information: \* if
the same :math:`\\theta` cut is applied at all energies and offsets, `a
`RAD_MAX`
keyword <https://gamma-astro-data-formats.readthedocs.io/en/latest/irfs/point_like/#rad-max>`__
is added to the header of the data units containing IRF components. This
should be used to define the size of the ON and OFF regions; \* in case
an energy- (and offset-) dependent :math:`\theta` cut is applied, its
values are stored in additional `FITS` data unit, named
``RAD_MAX_2D` <https://gamma-astro-data-formats.readthedocs.io/en/latest/irfs/point_like/#rad-max-2d>`__.

`Gammapy` provides a class to automatically read these values,
`~gammapy.irf.RadMax2D`, for both cases (fixed or energy-dependent
:math:`\theta` cut). In this notebook we will focus on how to perform a
spectral extraction with a point-like IRF with an energy-dependent
:math:`\theta` cut. We remark that in this case a
`~regions.PointSkyRegion` (and not a `~regions.CircleSkyRegion`)
should be used to define the ON region. If a geometry based on a
`~regions.PointSkyRegion` is fed to the spectra and the background
`Makers`, the latter will automatically use the values stored in the
`RAD_MAX` keyword / table for defining the size of the ON and OFF
regions.

Beside the definition of the ON region during the data reduction, the
remaining steps are identical to the other :doc:`/tutorials/analysis-1d/spectral_analysis`
tutorial., so we will not detail the data reduction steps already
presented in the other tutorial.

**Objective: perform the data reduction and analysis of 2 Crab Nebula
observations of MAGIC and fit the resulting datasets.**

Introduction
------------

We load two MAGIC observations in the
`gammapy-data <https://github.com/gammapy/gammapy-data>`__ containing
IRF component with a :math:`\theta` cut.

We define the ON region, this time as a `~regions.PointSkyRegion` instead of a
`CircleSkyRegion`, i.e. we specify only the center of our ON region.
We create a `RegionGeom` adding to the region the estimated energy
axis of the `~gammapy.datasets.SpectrumDataset` object we want to
produce. The corresponding dataset maker will automatically use the
:math:`\theta` values in `~gammapy.irf.RadMax2D` to set the
appropriate ON region sizes (based on the offset on the observation and
on the estimated energy binning).

In order to define the OFF regions it is recommended to use a
`~gammapy.makers.WobbleRegionsFinder`, that uses fixed positions for
the OFF regions. In the different estimated energy bins we will have OFF
regions centered at the same positions, but with changing size. As for
the `~gammapy.makers.SpectrumDatasetMaker`, the `~gammapy.makers.ReflectedRegionsBackgroundMaker` will use the
values in `~gammapy.irf.RadMax2D` to define the sizes of the OFF
regions.

Once the datasets with the ON and OFF counts are created, we can perform
a 1D likelihood fit, exactly as illustrated in the previous example.

"""

######################################################################
# Setup
# -----
#
# As usual, we’ll start with some setup …
#

import astropy.units as u
from astropy.coordinates import SkyCoord
from regions import PointSkyRegion

# %matplotlib inline
import matplotlib.pyplot as plt
from gammapy.data import DataStore
from gammapy.datasets import Datasets, SpectrumDataset
from gammapy.makers import (
    ReflectedRegionsBackgroundMaker,
    SafeMaskMaker,
    SpectrumDatasetMaker,
    WobbleRegionsFinder,
)
from gammapy.maps import Map, MapAxis, RegionGeom
from gammapy.modeling import Fit
from gammapy.modeling.models import (
    LogParabolaSpectralModel,
    SkyModel,
    create_crab_spectral_model,
)

######################################################################
# Check setup
# -----------
from gammapy.utils.check import check_tutorials_setup
from gammapy.visualization import plot_spectrum_datasets_off_regions

check_tutorials_setup()


######################################################################
# Load data
# ---------
#
# We load the two MAGIC observations of the Crab Nebula containing the
# `RAD_MAX_2D` table.
#

data_store = DataStore.from_dir("$GAMMAPY_DATA/magic/rad_max/data")
observations = data_store.get_observations(required_irf="point-like")


######################################################################
# A `RadMax2D` attribute, containing the `RAD_MAX_2D` table, is
# automatically loaded in the observation. As we can see from the IRF
# component axes, the table has a single offset value and 28 estimated
# energy values.
#

rad_max = observations["5029747"].rad_max
print(rad_max)


######################################################################
# We can also plot the rad max value against the energy:
#

rad_max.plot_rad_max_vs_energy()


######################################################################
# Define the ON region
# --------------------
#
# To use the `RAD_MAX_2D` values to define the sizes of the ON and OFF
# regions **it is necessary to specify the ON region as
# a `~regions.PointSkyRegion`:
#

target_position = SkyCoord(ra=83.63, dec=22.01, unit="deg", frame="icrs")
on_region = PointSkyRegion(target_position)


######################################################################
# Run data reduction chain
# ------------------------
#
# We begin with the configuration of the dataset maker classes:
#

# true and estimated energy axes
energy_axis = MapAxis.from_energy_bounds(
    50, 1e5, nbin=5, per_decade=True, unit="GeV", name="energy"
)
energy_axis_true = MapAxis.from_energy_bounds(
    10, 1e5, nbin=10, per_decade=True, unit="GeV", name="energy_true"
)

# geometry defining the ON region and SpectrumDataset based on it
geom = RegionGeom.create(region=on_region, axes=[energy_axis])

dataset_empty = SpectrumDataset.create(geom=geom, energy_axis_true=energy_axis_true)


######################################################################
# The `SpectrumDataset` is now based on a geometry consisting of a
# single coordinate and an estimated energy axis. The
# `SpectrumDatasetMaker` and `ReflectedRegionsBackgroundMaker` will
# take care of producing ON and OFF with the proper sizes, automatically
# adopting the :math:`\theta` values in `Observation.rad_max`.
#
# As explained in the introduction, we use a `WobbleRegionsFinder`, to
# determine the OFF positions. The parameter `n_off_positions` specifies
# the number of OFF regions to be considered.
#

dataset_maker = SpectrumDatasetMaker(
    containment_correction=False, selection=["counts", "exposure", "edisp"]
)

# tell the background maker to use the WobbleRegionsFinder, let us use 1 off
region_finder = WobbleRegionsFinder(n_off_regions=3)
bkg_maker = ReflectedRegionsBackgroundMaker(region_finder=region_finder)

# use the energy threshold specified in the DL3 files
safe_mask_masker = SafeMaskMaker(methods=["aeff-default"])

# %%time
datasets = Datasets()

# create a counts map for visualisation later...
counts = Map.create(skydir=target_position, width=3)

for observation in observations:
    dataset = dataset_maker.run(
        dataset_empty.copy(name=str(observation.obs_id)), observation
    )
    counts.fill_events(observation.events)
    dataset_on_off = bkg_maker.run(dataset, observation)
    dataset_on_off = safe_mask_masker.run(dataset_on_off, observation)
    datasets.append(dataset_on_off)


######################################################################
# No we can plot the off regions and target positions on top of the counts
# map:
#

ax = counts.plot()
geom.plot_region(ax=ax, kwargs_point={"color": "k", "marker": "*"})
plot_spectrum_datasets_off_regions(ax=ax, datasets=datasets)


######################################################################
# Fit spectrum
# ------------
#
# | We perform a joint likelihood fit of the two datasets.
# | For this particular datasets we select a fit range between
#   :math:`80\,{\rm GeV}` and :math:`20\,{\rm TeV}`.
#

e_min = 80 * u.GeV
e_max = 20 * u.TeV

for dataset in datasets:
    dataset.mask_fit = dataset.counts.geom.energy_mask(e_min, e_max)

spectral_model = LogParabolaSpectralModel(
    amplitude=1e-12 * u.Unit("cm-2 s-1 TeV-1"),
    alpha=2,
    beta=0.1,
    reference=1 * u.TeV,
)
model = SkyModel(spectral_model=spectral_model, name="crab")

datasets.models = [model]

fit = Fit()
result = fit.run(datasets=datasets)

# we make a copy here to compare it later
best_fit_model = model.copy()


######################################################################
# Fit quality and model residuals
# -------------------------------
#


######################################################################
# We can access the results dictionary to see if the fit converged:
#

print(result)


######################################################################
# and check the best-fit parameters
#

datasets.models.to_parameters_table()


######################################################################
# A simple way to inspect the model residuals is using the function
# `~SpectrumDataset.plot_fit()`
#

ax_spectrum, ax_residuals = datasets[0].plot_fit()
ax_spectrum.set_ylim(0.1, 120)


######################################################################
# For more ways of assessing fit quality, please refer to the dedicated
# `modeling and fitting tutorial :doc:`/tutorials/api/fitting` tutorial.
#


######################################################################
# Compare against the literature
# ------------------------------
#
# Let us compare the spectrum we obtained against a `previous measurement
# by
# MAGIC <https://ui.adsabs.harvard.edu/abs/2015JHEAp...5...30A/abstract>`__.
#

plot_kwargs = {
    "energy_bounds": [0.08, 20] * u.TeV,
    "sed_type": "e2dnde",
    "yunits": u.Unit("TeV cm-2 s-1"),
    "xunits": u.GeV,
}

crab_magic_lp = create_crab_spectral_model("magic_lp")

best_fit_model.spectral_model.plot(
    ls="-", lw=1.5, color="crimson", label="best fit", **plot_kwargs
)
best_fit_model.spectral_model.plot_error(facecolor="crimson", alpha=0.4, **plot_kwargs)
crab_magic_lp.plot(ls="--", lw=1.5, color="k", label="MAGIC reference", **plot_kwargs)

plt.legend()
plt.ylim([1e-13, 1e-10])